MATHEMATICS HIGH SCHOOL

The time , in hours , it takes to repair an electrical breakdown in a certain factory is represent by a random variable x where repair time follow a normal distribution with mean 5 hour and standard deviation 1 hour , if 5 electrical breakdown ore randomly chosen , Find the probability that ( a all repaired time below 6 hours ( b ) exactly 3 of them repaired below 6 hours

Answers

Answer 1

Answer:

Answer:

a) 0.4215 = 42.15% probability that all are repaired in less than 6 hours.

b) 0.15 = 15% probability that exactly 3 of them repaired in a time below 6 hours

Step-by-step explanation:

To solve this question, we need to understand the normal and the binomial probability distributions.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)$

In which $C_(n,x)$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_(n,x) = (n!)/(x!(n-x)!)$

And p is the probability of X happening.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = (X - \mu)/(\sigma)$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Proportion repaired below 6 hours:

Mean 5 hours and standard deviation 1 hour, which means that $\mu = 5, \sigma = 1$

This proportion is the p-value of Z when X = 6. So

$Z = (X - \mu)/(\sigma)$

$Z = (6 - 5)/(1)$

$Z = 1$

$Z = 1$ has a p-value of 0.8413.

0.8413 repaired below 6 hours.

For the binomial distribution, this means that $p = 0.8413$

5 are chosen:

This means that $n = 5$

a) Probability that all are repaired in less than 6 hours

This is P(X = 5). So

$P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)$

$P(X = 5) = C_(5,5).(0.8413)^(5).(0.1587)^(0) = 0.4215$

0.4215 = 42.15% probability that all are repaired in less than 6 hours.

b) Probability that exactly 3 of them repaired below 6 hours

This is P(X = 3). So

$P(X = x) = C_(n,x).p^(x).(1-p)^(n-x)$

$P(X = 3) = C_(5,3).(0.8413)^(3).(0.1587)^(2) = 0.15$

0.15 = 15% probability that exactly 3 of them repaired in a time below 6 hours

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Camille uses a 20% off coupon when buying a sweater that costs $47.99. If she also pays 6% sales tax on the purchase, how much does she pay?

Answers

47.99-20%×47.99= $38.392 = a (price after being discounted)

Final price = a+ 6%×a = $40.69552

If f(x)=3x+7 and g(x)=2x-5 find g(f(-3))

A. -26 B.-9 C. -1 D. 10

Answers

The value of g(f(-3)) would be -9 which is the correct answer would be an option (B).

What exactly is a function?

A function is defined as a mathematical phrase that specifies a connection between two variables in algebra.

We have been given the functions below as

f(x) = 3x + 7 and g(x) = 2x - 5

We have to determine the value of g(f(-3))

Substitute the value of f(x) = 3x + 7 in the g(x) = 2x - 5 to get g(f(x))

⇒ g(f(x)) = 2(3x + 7) - 5

Apply the distributive property of multiplication,

⇒ g(f(x)) = 6x + 14 - 5

⇒ g(f(x)) = 6x + 9

Substitute the value of x = -3 in the g(x) = 2x - 5 to get g(f(-3))

⇒ g(f(-3)) = 6(-3) + 9

⇒ g(f(-3)) = -18 + 9

⇒ g(f(-3)) = -9

Therefore, the value of g(f(-3)) would be -9.

Learn more about the functions here:

brainly.com/question/12431044

#SPJ1

$f(x)=3x+7 \n g(x)=2x-5 \n \n g(f(-3)) = ? \n \nf(-3)=3x+7 =3 \cdot (-3)+7=-9+7=-2 \n \n g(-2)=2x-5 =2*(-2)-5=-4-5 = -9\n \n g(f(-3)) = -9 \n \n Answer: \ B.) \ \ -9$

Are the expressions (4x)^2 and 4x^2 equal in value? How would you explain your answer?

Answers

understand pemdas
parenthasees
exponenets
multiiplication or dividsion
additon or subtraction

(4x)^2=4x times 4x
4x^2=4 times x times x=4(x^2)

(4x)^2=16x^2
4x^2=4(x^2)
values are not equal
(just for fun: 4x^2=(2x)^2)

What is the sum of all of the odd numbers from 1 to 59?

Answers

Answer:

sum = 900

Step-by-step explanation:

The sum of all odd number can be solved using arithmetic progression formula.

Odd numbers are numbers that cannot be exactly divided by 2 .That means odd number have remainder when divide by 2.

The first odd number is 1

The second is 3

The sequence goes like this

1, 3, 5, 7, 9, 11, 13, 15, 17, 19 , 21 .................................59

a = 1

d = 2

where

a = first term

d = common difference

let us find the number of terms before finding the sum

nth term = a + (n - 1)d

59 = 1 + (n - 1)2

59 = 1 + 2n - 2

59 + 2 - 1 = 2n

60 = 2n

n = 60/2

n = 30

Sum = n/2(a+L)

where L = last term

sum = 30/2(1 + 59)

sum = 15(60)

sum = 900

arith. series for odd number
An = 1 + 2(n-1) ; A1 = 1

sum to n terms
Sn = (An + A1)n/2 ;
An=59, n = 29

The state of Colorado is shaped like a rectangle with an approximate width of 280 mi and length of 380 mi. What is the population density of Colorado in people per square mile if the population is 5,116,800?

Answers

The population density of Colorado is 48.09 people per mile²

Population density

Population density is the concentration of individuals within a specific area. It is given by:

Population density = number of people / land area

Land area = length * width = 280 * 380 = 106400 mile²

Population density = 5,116,800 / 106400 = 48.09 people per mile²

The population density of Colorado is 48.09 people per mile²

Find out more in Population density at: brainly.com/question/13902749

Answer:

Step-by-step explanation:

160miles • 330miles= 52,800square miles

Now it wants the population density in people per square miles, so you need to divide the population by the number of square miles.

4779736/52800=90.5 which is about 91people per square mile.

cone A has a height of 3 meters and radius of 2 meters. Cone B has the same radius, but height og 6 meters, calculate the volume of each cone. Which conclusion is correct ? The volume of cone A is twice the volume of cone B, the volume of cone Bis ywice the volume of cone A , The volume of cone B is 4 time the volume of cone A or The volume of cone B is 3 times the volume of cone A?